Describe, at a high level, a one$-$tape deterministic Turing machine that will accept

an input string if and only if it is in the following language:

L $=\{$a

mb

nx $|$ m$,$ n in Z

nonneg, x in $\{$c$,$ d$\}$

$$

$,$ nc$($x$)=$ m$,$ nd$($x$)=$ n$\}$